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<p>Group classification is the basic problem inthe group analysis of differential equations with an&#xa0;arbitrary element.For the equations of ideal gas dynamicswith a&#xa0;stationary state equation the problem is solved witha&#xa0;brute-force search of simplifications of the defining relationsby equivalence transformations.For time-dependent relaxation state equations,the brute-force search is huge,and we have to use an&#xa0;optimal system of subalgebrasof a&#xa0;subalgebra extending the core of admitted algebras.Some combination of both methods leads to a&#xa0;solution ofthe problem of group classification of gas-dynamic relaxation.</p>

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Group Classification of Ideal Gas-Dynamic Relaxing Media by the Method of an Optimal System of Subalgebras

  • 期刊论文

  • 发表日期：

    2025年1月29日

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  • S. V. Khabirov

摘要

Group classification is the basic problem inthe group analysis of differential equations with an arbitrary element.For the equations of ideal gas dynamicswith a stationary state equation the problem is solved witha brute-force search of simplifications of the defining relationsby equivalence transformations.For time-dependent relaxation state equations,the brute-force search is huge,and we have to use an optimal system of subalgebrasof a subalgebra extending the core of admitted algebras.Some combination of both methods leads to a solution ofthe problem of group classification of gas-dynamic relaxation.